However, one important open problem that remains is to find the amplitude of the oscillations that result from the Hopf bifurcations. Instability in a queueing system causes queue lengths to oscillate with time which can lead to inefficienies due to some servers being overworked and others being underworked. Being able to compute the amplitude of the queue length oscillations could help a service manager quantify the level of ineffiency present due to the system's instability. Typically oscillations in systems with delays are calculated approximately by a method called Lindstedt's method. In fact, how to approximate the amplitude of oscillations in queueing systems with delays is outlined in [1]}. Despite the analysis carried out in [1]} it still remains an open question to compute the amplitude of oscillations in the FDE model we study in this paper. The main reason is that the delay is non-stationary with respect to time, which renders the Lindstedt approach ineffective. A new approach must be derived, which is the main focus of this work. Thus, in this paper, we answer the following question: when oscillations occur, how does the amplitude of the oscillations depend on the model parameters?
